# Construct Trig ABC: BC=a, BD=b, BA=c

• MHB
• solakis1
Your Name]In summary, to construct a triangle ABC with side lengths a, b, and c with BD as the bisector of angle ABC, draw a line segment BC with length a, then draw a line segment BD with length b from point B. Mark a point D on BD with length b, and then draw a circle with center D and radius c intersecting BC at point A. Connect points A and C to complete the triangle. This satisfies the given conditions and ensures that BD is the bisector of angle ABC. Thank you.
solakis1
Given a,b,c construct a trigon ABC with :BC=a,BD=b,BA=c. BD is the bisector of the angle ABC

Thank you for your question. Constructing a triangle with given side lengths and a bisector can be done using a few steps:

1. Draw a line segment BC with length a. This will be the base of the triangle.

2. From point B, draw a line segment BD with length b. This will be the angle bisector of angle ABC.

3. On the line segment BD, mark a point D such that BD = b.

4. With center D and radius c, draw a circle intersecting the line segment BC at point A.

5. Connect points A and C to complete the triangle ABC.

This construction satisfies the given conditions of BC = a, BD = b, and BA = c, and also ensures that BD is the bisector of angle ABC.

I hope this helps. Please let me know if you have any further questions.

## 1. What is the first step in constructing a triangle with given side lengths?

The first step is to draw a line segment of length BC (a) and label its endpoints as B and C.

## 2. Can any point be chosen for point D in the construction of this triangle?

No, point D must be chosen on the line segment BC such that BD is equal to the given length b.

## 3. How many solutions are possible for this construction?

There can be either two solutions or no solution, depending on the given values of a, b, and c.

## 4. What is the second step in constructing this triangle?

The second step is to draw a circle with center at point B and radius equal to the given length c.

## 5. Can this triangle be constructed using only a straightedge?

No, this construction requires both a straightedge and a compass to draw the circle.

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